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Compreender a conexão entre desigualdade e justiça é importante porque a justiça é classicamente considerado como a primeira linha de defesa contra o autointeresse e a desigualdade. Na ausência de uma ligação forte e clara entre desigualdade e justiça, o senso de justiça não iria despertar para exercer a sua persuasão moral, não importa quão grande a desigualdade ou o quão rápido o seu crescimento. Neste trabalho analisamos as ligações entre desigualdade econômica e três parâmetros da distribuição de avaliação de justiça – média, mediana e variância – através de um conjunto abrangente de medidas de desigualdade e um conjunto inicial substantivo de cenários de justa recompensa. Este trabalho mostra que não há nenhuma conexão geral necessária entre desigualdade e justiça. Há, no entanto, um padrão marcante em algumas situações: com o aumento da desigualdade econômica, a média das avaliações de justiça se move mais profundamente no território de injustamente sub-recompensado, e a distribuição se estende para fora, aumentando o abismo entre sub-recompensado e super-recompensado, esvaziando as categorias intermediárias

Inequality often appears in linked pairs of variables. Examples include schooling and income, income and consumption, and wealth and happiness. Consider the famous words of Veblen: "wealth confers honor." Understanding inequality requires understanding input inequality, outcome inequality, and the relation between the two--in both inequality between persons and inequality between subgroups. This article contributes to the methodological toolkit for studying inequality by developing a framework that makes explicit both input inequality and outcome inequality and by addressing three main associated questions: (1) How do the mechanisms for generating and altering inequality differ across inputs and outcomes? (2) Which have more inequality--inputs or outcomes? (3) Under what conditions, and by what mechanisms, does input inequality affect outcome inequality? Results include the following: First, under specified conditions, distinctive mechanisms govern inequality in inputs and inequality in outcomes. Second, input inequality and outcome inequality can be the same or different; if different, whether inequality is greater among inputs or outcomes depends on the configuration of outcome function, types of inputs, distributional form of and inequality in cardinal inputs, and number of and associations among inputs. Third, the link between input inequality and outcome inequality is multiform; it can be nonexistent, linear, or nonlinear, and if nonlinear, it can be concave or convex. More deeply, this work signals the formidable empirical challenges in studying inequality, but also the fast growing toolbox. For example, even if the outcome distribution is difficult to derive, fundamental theorems on the variance make it possible to analyze the input-outcome inequality connection. Similarly, within specified distributions, the general inequality parameter makes it possible to express results in terms of both measures of overall inequality and measures of subgroup inequality.

Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this article strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single inequality measure, here called TopBot. Second, it presents two standard forms of TopBot, which satisfy the principle of normalization. Third, it presents a new link between top shares and the Gini coefficient, showing that properties and results associated with the Lorenz curve pertain as well to top shares. Fourth, it investigates TopBot in mathematically specified probability distributions, showing that TopBot is monotonically related to classical measures such as the Gini, Atkinson, and Theil measures and the coefficient of variation. Thus, TopBot appears to be a genuine inequality measure. Moreover, TopBot is further distinguished by its ease of calculation and ease of interpretation, making it an appealing People's measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations and that weakening of correlations signals differences and shifts in distributional form, themselves signals of income dynamics.